Have you asked your vet specifically for a recommendation of an acceptable treat for your pup? I know the vet said to give her the prescription canned food only. However, perhaps he/she was only thinking of what would be easiest for you and didn’t think about how important treats are to your girl’s emotional health. The vet might okay some kind of treat if you explained how important treats are to her overall well-being.
The carrots actually sound like a good option. They don’t contain any fat, and a small amount might not disagree with her sensitive stomach. There are also treats made especially for dogs with digestive issues, for instance:
https://www.petco.com/shop/en/petcos...-canine-treats